题目

sinx+cosx=m(m的绝对值

提问时间：2020-09-18

答案

sinx+cosx=m
两边平方得
1+2sinxcosx=m^2
sinxcosx=(m^2-1)/2
sin^3x+cos^3x
=(sinx+cosx)[(sinx)^2-sinxcosx+(cosx)^2]
=m*[(sinx+cosx)^2-3sinxcosx]
=m*(m^2-3(m^2-1)/2)
=m*(-m^2/2+3/2)
=-m^3/2+3m/2
sin^4x+cos^4x
=[(sinx)^2+(cosx)^2]-2(sinxcosx)^2
=1-2[(m^2-1)/2]^2
=1-(1/2)(m^4-2m^2+1)
=-(1/2)(m^4-2m^2+1)